Chapter 9 Introduction

Transcription

1 Chapter 9 Introduction 9.1 Historical Remarks 9.2 The Principles of Guidance, Naviga@on and Control 9.3 Setpoint Regula@on, Trajectory- Tracking and Path- Following 9.4 Control of Underactuated and Fully Actuated CraL Part II of the book deals with the design of model- based GNC systems. The theory and cases studies are organized as four independent chapters: Chapter 10: Guidance Systems: Systems for automa@cally guiding the path of a marine cral, usually without direct or con@nuous human control. Chapter 11: Sensor and Naviga:on Systems: Systems for determina@on of the cral's posi@on/astude, velocity and accelera@on. Chapter 12: Mo:on Control Systems: PID design methods for automa@c control of posi@on/astude, velocity and accelera@on. This involves control systems for stabiliza@on, trajectory- tracking and path- following control of marine cral. Chapter 13: Advanced Mo:on Control Systems: Design of advanced mo@on control systems using op@mal and nonlinear control theory. 1

2 9.2 The Principles of Guidance, Navigation and Control A mo@on control system is usually constructed as three independent blocks denoted as the guidance, naviga,on and control (GNC) systems. These systems interact with each other through data and signal transmission. In the figure, the guidance system makes use of the es@mated alterna@vely measured posi@ons and veloci@es. This is referred to as a closed- loop guidance system while a guidance system that only use reference feedforward (no feedback) is an open- loop guidance system. 2

3 9.2 The Principles of Guidance, Navigation and Control Guidance is the or the system that computes the reference (desired) velocity and of a marine cral to be used by the mo@on control system. These data are usually provided to the human operator and the naviga@on system. The basic components of a guidance system are: Mo,on sensors External data such as weather data (wind speed/direc,on, wave height/slope, current speed/direc,on) Computer The computer collects and processes the informa@on, and then feeds the results to the mo@on control system. In many cases, advanced op@miza@on techniques are used to compute the op@mal trajectory or path for the marine cral to follow. This might include sophis@cated features such as fuel op@miza@on, naviga@on, weather rou@ng, collision avoidance, forma@on control and synchroniza@on. Copyright Bjarne Stenberg/NTNU 3

4 9.2 The Principles of Guidance, Navigation and Control is the science of a cral by determining its course and distance traveled. In some cases velocity and are determined as well. This is usually done by using a global naviga,on satellite system (GNSS) combined with mo@on sensors such as accelerometers and gyros. The most advanced naviga@on system for marine applica@ons is the iner,al naviga,on system (INS). Naviga@on is derived from the La@n navis, ship, and agere, to drive. It originally denoted the art of ship driving, including steering and sesng the sails. The skill is even more ancient than the word itself, and it has evolved over the course of many centuries into a technological science that encompasses the planning and execu@on of and economical opera@on of ships, underwater vehicles, aircral and spacecral. Copyright Bjarne Stenberg/NTNU 4

5 9.2 The Principles of Guidance, Navigation and Control Control, or more specifically control, is the of determining the necessary control forces and moments to be provided by the cral in order to a certain control The desired control is usually seen in with the guidance system. Examples of control are: Minimum energy Setpoint regula,on Trajectory- tracking control Path- following control Maneuvering control Copyright Bjarne Stenberg/SINTEF the control algorithm involves the design of feedback and feedforward control laws. The outputs from the system, velocity and are used for feedback control while feedforward control is implemented using signals available in the guidance system and other external sensors. 5

6 9.3 Setpoint Regulation,Trajectory-Tracking and Path- Following Control When designing control systems, the control must be well defined in order to the requirement for safe of the cral. It is important to between the following three important control Setpoint The most basic guidance system is a constant input or setpoint provided by a human operator. The corresponding controller will then be a regulator. Examples of setpoint regula@on are constant depth, trim, heel and speed control. It could also be regula@on to zero (sta,onkeeping). Trajectory- Tracking Control: The posi@on and velocity of the marine cral should track varying posi@on and velocity reference signals. The corresponding feedback controller is a trajectory- tracking controller. Tracking control can be used for course- changing maneuvers, speed- changing and astude control. Path- Following Control: This is to follow a predefined path independent (no temporal constraints). Moreover no restric@ons are placed on the temporal propaga@on along the path. This is typical for ships in transit between con@nents or underwater vehicles used to map the seabed. 6

7 9.4 Control of Underactuated and Fully Actuated Craft When designing control systems for marine cral, it is important to between: Underactuated Marine CraL Fully Actuated Marine CraL It is trivial to control a fully actuated marine cral while underactua@on puts limita@ons on what control objec@ves that can be sa@sfied. Copyright Bjarne Stenberg/MARINTEK Defini:on 9.1 (Degrees of Freedom (DOF)) For a marine crag, DOF is the set of independent displacements and rota,ons that completely specify the displaced posi,on and orienta,on of the crag. A crag that can move freely in the 3- D space has maximum 6 DOFs three transla,onal and three rota,onal components. 7 Consequently, a fully actuated marine cral opera@ng in 6 DOF must be equipped with actuators that can produce independent forces and moments in all direc@ons. When simula@ng the mo@on of such a cral, a total of 12 ODEs are needed since the order of the system is: order! 2! DOF

8 9.4.1 Configuration Space Control systems for underactuated and fully actuated marine cral are designed by defining a workspace in which the control objec@ve is specified. Defini:on 9.2 (Configura:on Space) The n- dimensional configura,on space is the space of possible posi,ons and orienta,ons that a crag may apain, possibly subject to external constraints. The configura@on of a marine cral can be uniquely described by an n- dimensional vector of generalized coordinate that is, the least number of coordinates needed to specify the state of the system. If there exists k geometric constraints: h i!!"! 0 i! 1,..,k the possible mo@ons of the cral is restricted to an (n- k)- dimensional submanifold. 8

9 9.4.1 Configuration Space 9

10 9.4.1 Configuration Space Defini:on 9.3 (Underactuated Marine CraJ) A marine crag is underactuated if it has less control inputs than generalized coordinates (r < n) Defini:on 9.4 (Fully Actuated Marine CraJ) A marine crag is fully actuated if it has equal or more control inputs than generalized coordinates (r n) From this is follows that a marine cral which operates in n DOF has a configura@on space of dimension: dim(η) = n If the cral only has actuators in surge, sway and yaw, the cral is underactuated in sense of opera@on in 6 DOF while the design of a mo@on control system for the horizontal plane mo@on (DP system) can be achieved using only three control inputs. Underwater vehicles that have actuators that produces independent forces and moments in 6 DOF are fully actuated. Formulate the control objec@ve in a workspace of dimension m < n instead of the n dimensional space. Hence, only m actuators are needed. 10

11 9.4.2 Workspace and Control Objectives Defini:on 9.5 (Workspace) The workspace is a reduced space of dimension m < n in which the control objec,ve is defined. The workspace of a conven@onal heading autopilot system is m = 1 since only the yaw mo@on is controlled. The workspace of a horizontal plane controller, for instance a DP system controlling the mo@ons in surge, sway and yaw, is m = 3 If r is the number of independently controlled actuators spanning different direc@ons in the n- dimensional configura@on space, then: Full actua@on means that independent control forces and moments are simultaneously available in all direc@ons. Moreover, all posi@ons in the configura@on space have actua@on such that r = n An underactuated marine cral has independent control forces and moments in only some DOF. Moreover, r < n. Stabilizing and tracking controllers for underactuated cral are usually designed by considering a workspace of dimension r < n sa@sfying m = r (fully actuated in the workspace but not in the configura@on space) Underactuated control is a technical term used in control theory to describe a mo@on control system for a cral that is underactuated in the workspace (r < m). To design a control system that achieves stabiliza@on, trajectory- tracking and path- following control for this case is nontrivial and NOT used in prac@cal systems. Hence, this is not discussed in this book. 11

12 9.4.2 Workspace and Control Objectives 12

13 9.4.3 Weathervaning of Underactuated Craft in a Uniform Force Field Marine cral are usually controlled in surge, sway and yaw by using three controls. However, unlike wheeled cars and other cral opera@ng on the surface of the Earth, it is possible to stabilize the posi@ons of a marine cral by means of two controls. The main reason for this is that marine cral are exposed to dril forces generated by waves, wind and ocean currents. This means that the equa@ons of mo@on are forced. For sta@onkeeping, it is common to assume that the dril forces are slowly varying such that the resul@ng component due to wind, waves and ocean currents can be treated as a constant uniform force. Hence, a marine cral can be modeled as a rigid- body opera@ng in a unified force field similar to a pendulum in the gravity field (Fossen and Strand 2001). 13

14 9.4.3 Weathervaning of Underactuated Craft in a Uniform Force Field It is possible to stabilize a marine cral in a uniformed force field using only two controls (r = 2) even though the configura@on space of the cral is surge, sway and yaw ( m = 3) The Beauty of Weathervaning Use one controller to compensate for the dril force that acts along the longitudinal axis of the body. Use one controller to align the cral to the force field. This is similar to a weathervane which is aligned to the force field created by the wind. Mo@on control systems can be designed to behave such as a weathervane and they are used offshore for sta@onkeeping of supply vessels and tankers near floa@ng structures in order to save energy. The drawback is that sta@onkeeping using only two controls implies that the desired heading cannot be specified arbitrarily. Simultaneously control of the mo@ons in surge, sway and yaw to arbitrarily values requires three controls. 14